C₁₃×D₁₅×D₃₅ #41032017

order	27300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

C₁₃×D₁₅×D₃₅

	subgroup	G/H
center, hypercenter	C₁₃	D₁₅×D₃₅
commutator, cosocle, hypocenter	C₃×C₅²×C₇	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₃	C₂²
LCS	G ▷ C₃×C₅²×C₇
UCS	C₁ ◁ C₁₃

192 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 2730

2223 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 907);